Information of a qubit interacting with a multilevel environment

We consider the interaction of a small quantum system (a qubit) with a structured environment consisting on many levels. The qubit will experience a decoherence process, which implies that its initial information will be transferred to the environment. We investigate how this information is distributed on a given subset of levels as a function of its size, using the mutual information between both entities, in the spirit of the partial information plots studied by Zurek. In this case we observe some differences, which arise from the fact that we are partitioning just one quantum system, and not a collection of them. However some similar features, like a redundancy (in the sense that a given amount of information is shared by many subsets), which increases with the size of the environment, are also found here.